192 THE INCREMENT. 



This is the capital, which it is jiroposed to let work for 

 another n years. During that period, it increases to the value 

 of the forest in the year //) + ii, from which amount must he 

 deducted the annual costs during ;/ years with compound 

 interest, so that — 



W= r,„^„ + S-E a-Op" - 1) 

 and 



100 



("\/^ 



Y^+S 



— 1 



If, between the years m and m + », a thinning has been 

 made, say in the year x, its value, with compound interest 

 to the year m + «, must be added to TF, so that the formula 

 becomes : — 



cur ^loof A/Yn,+n + T.XrOp"+"-" + S-E(10p "-l)_^Y 



In either case, the value S of the soil can be taken as the 

 cost value or as the expectation value. 



If n is placed = 1, the above formula reduces to — 



C-0-. ,. _ (r,„+i - r,„ - (') X 100 



^' y::-rs ' 



agreeing with that given at page 165 for the current annual 

 forest per cent. 



Example. — Taking the data in the table at page 120, and 

 putting j; = 2i per cent., S = 404 shillings, c = 3 shillings, 

 the following values of pj are obtained : — 



For the period 70 — 80 years : — 



log (100+;v) = 



.^ I log (2.860 + 144 + 404 — 84) — log (1,H87 + 404) 

 "^ 10 



^o-^"^),. = 2-G8. 



* This i'oi'iimla ditfeis lioui that given by Presslur and Jiideich for the reasons 

 indicated in the footnote at jiage 159. 



